Primary Mathematics: Fractions & Basic Algebra — Complete Lesson Notes

WHAT'S INSIDE THIS PACK A complete Primary 4-6 lesson-notes pack (NERDC-aligned) with 6 units. Each unit has easy-to-read explanations, step-by-step worked examples, and practice exercises with full answers at the end. UNIT 1 – UNDERSTANDING FRACTIONS Lesson 1.1 What a fraction means A fraction shows a part of a whole. The number at the top (numerator) counts the parts you have; the number at the bottom (denominator) tells how many equal parts the whole was divided into. Example: In 3/5, the whole is divided into 5 equal parts and you have 3 of them. Lesson 1.2 Equivalent fractions Two fractions are equivalent when they stand for the same amount. Multiply or divide the top and the bottom by the same number. Example: 1/2 = 2/4 = 4/8 (multiply top and bottom by the same number). Lesson 1.3 Comparing and ordering fractions With the same denominator, the bigger numerator is the bigger fraction. With different denominators, first change them to a common denominator, then compare. UNIT 2 – ADDITION AND SUBTRACTION OF FRACTIONS RULES - To add or subtract fractions, use the same denominator first (use the LCM of the denominators). - Then add or subtract the numerators only. - Write the answer in its simplest (lowest) form. Worked example: 1/4 + 3/8 LCM of 4 and 8 is 8. 1/4 becomes 2/8. So 2/8 + 3/8 = 5/8. Answer: 5/8. UNIT 3 – MULTIPLICATION AND DIVISION OF FRACTIONS Lesson 3.1 Multiplying fractions Multiply straight across: numerators together, denominators together. Always simplify at the end. Lesson 3.2 Dividing fractions Invert (flip) the second fraction, then multiply. This is the same as multiplying by its reciprocal. UNIT 4 – DECIMALS AND PERCENTAGES Lesson 4.1 Fractions to decimals Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Lesson 4.2 Decimals to percentages Multiply by 100. Example: 0.75 x 100 = 75%. Lesson 4.3 Real-life applications Discounts, test scores, and interest all use percentages. Practice converting between fraction, decimal and percentage in the exercises. UNIT 5 – INTRODUCTION TO ALGEBRA Lesson 5.1 Letters stand for numbers Use a letter (like x) to stand for a number you do not know yet. Example: "I think of a number and add 5. The result is 12." The number is x. x + 5 = 12, so x = 7. Lesson 5.2 Solving simple equations Do the same thing to both sides. To undo adding, subtract; to undo multiplying, divide. Worked example: 2x + 3 = 11. Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Lesson 5.3 Writing algebraic expressions Translate words into expressions: "three times a number" = 3n; "a number decreased by two" = n - 2. UNIT 6 – SHAPES, MEASUREMENT AND DATA Lesson 6.1 Perimeter and area Perimeter = distance around a shape. Area of a rectangle = length x breadth. Lesson 6.2 Reading simple graphs Read bar charts and line graphs; interpret and compare data. Lesson 6.3 Money problems Word problems on shopping, savings and change, applying addition, subtraction and percentages. PRACTICE EXERCISES (with answers at the end of the pack) 1. Write 3 equivalent fractions for 2/3. 2. Put 3/4, 1/2 and 5/8 in order from smallest to largest. 3. Calculate 2/5 + 1/10. 4. Calculate 7/8 - 1/4. 5. Multiply 3/5 x 2/3 and simplify. 6. Divide 5/6 by 2/3. 7. Convert 1/8 to a decimal and to a percentage. 8. Solve x + 6 = 15. 9. Solve 3x = 27. 10. A rectangle is 9 cm long and 4 cm wide. Find its perimeter and its area. FULL WORKED ANSWERS INCLUDED The pack ends with step-by-step solutions to all 10 exercises so a parent, tutor or learner can check work instantly.